The Application of a Sensitivity Method in the Power Quality Analysis of a Three-Phase Circuit

Non-sinusoidal operating conditions are frequently present in modern power systems and can adversely affect the normal operation and performance of industrial equipment connected to the electrical grid. This paper presents a method for evaluating the relationship between the harmonic weights of voltage and current and the sensitivities of reactive and apparent power under these conditions. These conditions primarily arise from non-linear loads and circuit components, particularly power electronic converters and other power electronic devices. In practical industrial environments, the harmonic composition of voltage and current may vary considerably, leading to significant changes in their RMS values and consequently affecting power transfer and overall power quality. The proposed approach first establishes the mathematical dependencies between active, reactive, and apparent power and the harmonic components of voltage and current. Based on these relationships, the sensitivities of the power quantities can be determined when one or more system parameters undergo variations. To validate the proposed methodology, we developed and implemented a numerical algorithm in MATLAB/Simulink for a practical industrial case. We compare the sensitivities obtained using the proposed approach with those calculated directly from measured data. The small differences between the two sets of results confirm the method’s accuracy and show that it is suitable for assessing harmonic variations on power quantities in non-sinusoidal power systems.